The Magpies, targeting a fifth win in their last six Premier League meetings with the Red Devils, fell behind before the half-hour mark following Dorgu's clinical volley at Old Trafford.
Despite a dominant second-half display from the visitors, with Lewis Hall hitting the crossbar, Eddie Howe marked his 200th game as United head coach with a narrow defeat in the club's penultimate game of 2025.
Newcastle, unchanged from last weekend's 2-2 draw against Chelsea, faced an early threat from the hosts as an unmarked Casemiro headed over from Mason Mount's in-swinging corner at the front post.
Man United, situated three points above the Magpies before kick-off, went close to taking the lead as Dorgu's dangerous pass from the right flank found Benjamin Šeško inside the box but the Slovenian striker elected to control the ball before directing his resulting effort wide of the left-hand post.
Bruno Guimarães, captaining the visitors, almost fired the Magpies in front after latching onto Sandro Tonali's inviting corner towards the front post before the Brazilian's glancing header was pushed away by Man United goalkeeper Senne Lammens.
Newcastle, however, fell behind in the 24th minute through Dorgu's clinical strike. After a long throw into the penalty area was only cleared into the defender's path by Nick Woltemade, the Dane hammered a first-time effort into the bottom left-hand corner.
United goalkeeper Aaron Ramsdale produced an important stop to prevent Dorgu netting his and Man United's second goal of the night as the Red Devils wing back collected Mateus Cunha's forward pass and, after driving into the box, his low drive at goal was parried by the Magpies shot-stopper before Fabian Schär hooked the loose ball clear to safety.
In the opening minutes of the second-half, Schär was narrowly close to levelling for the Magpies as Lewis Miley's lofted corner found the Swiss defender at the back post, who controlled the ball with his chest before his powerful drive was blocked by Dorgu, deflecting wide of the right-hand post.
Newcastle were fortunate not to fall further behind on the hour as Šeško hit the bar for the Red Devils. After Manuel Ugarte dispossessed Guimarães in a dangerous position, the ball found its way to the Man United striker who slammed a fierce effort onto the woodwork.
The Magpies struck the crossbar shortly after through Hall as the left-back, who had scored twice in his last three trips to Old Trafford, picked the ball up from distance before the 21-year-old's dipping effort from the edge of the box cannoned off the underside of the bar.
A frantic passage of play continued as Newcastle were left appealing for a penalty when Schär saw a shot inside a crowded penalty area blocked by Lisandro Martinez's arm but despite a VAR review, the on-field decision by referee Anthony Taylor stood.
The visitors, dominating large parts of possession in the second-half, continued to push for an equaliser as Anthony Gordon missed a glorious opportunity to net his eighth goal of the season in all competitions, latching onto Jacob Murphy's neat pass before the left winger dragged a low effort wide of the far post.
Gordon spurned another glorious chance in the final stages as a neat attacking move involving Lewis Miley, Guimarães and substitute Harvey Barnes saw the latter tee up Gordon but the Liverpool-born winger fired a wild effort over the crossbar.
With the full-time whistle approaching, Miley went close to netting a third goal in his last five competitive matches as the 19-year-old controlled Hall's cross from the left byline but the Stanley-born youngster's strike rose over the crossbar.
Newcastle United: Aaron Ramsdale, Lewis Hall, Fabian Schär, Sandro Tonali (Joe Willock 77), Anthony Gordon, Malick Thiaw, Jacob Murphy (Harvey Barnes 68), Nick Woltemade (Yoane Wissa 68), Bruno Guimarães (c), Jacob Ramsey (Joelinton 68), Lewis Miley.
Substitutes: Nick Pope, Alex Murphy, Leo Shahar, Sean Neave, Sam Alabi.
